The suspect Sheila is described to the police as being 5 feet, 4 inches, but when the bulletin is sent out on the teletype, it is given as 5 feet, 2 inches.
When the mayor is pressuring the drug companies for more vaccine one the company executives say that they need more needles. The mayor then instructs his secretary to contact sewing supply manufacturers for needles. Sewing needles are not hollow and cannot be used to deliver medication.
However, smallpox vaccine was delivered via a bifurcated-point solid needle using many small pinpricks to the skin that can be manufactured by such companies, and was.
The story takes place in 1947, but the Mayor of NYC has a 1950 round screen Zenith Television in his office. NYC had television in 1947, but screens were still much smaller.
Although the story takes place in New York City, where much of it was filmed, the finale was photographed in the 300 block of South Broadway, Los Angeles, easily identified by the flashing neon marquees of the Central and Cozy Theatres which were located there.
When Sheila is convinced to go to the clinic, the nurse offers her a glass of water. That would not be done if her temperature had to be taken. It would possibly give a false reading. Plus, any good nurse would have spotted her as "sick" the moment she laid eyes on Sheila.